Mechanics of adhesive contact on a power-law graded elastic half-space

We consider adhesive contact between a rigid sphere of radius R and a graded elastic half-space with Young's modulus varying with depth according to a power law E = E-0(z/c(0))(k) (0 < k < 1) while Poisson's ratio v remaining a constant. Closed-form analytical solutions are established for the critical force, the critical radius of contact area and the critical interfacial stress at pull-off. We highlight that the pull-off force has a simple solution of P-cr= -(k+3)pi R Delta gamma/2 where Delta gamma is the work of adhesion and make further discussions with respect to three interesting limits: the classical JKR solution when k = 0, the Gibson solid when k --> 1 and v = 0.5, and the strength limit in which the interfacial stress reaches the theoretical strength of adhesion at pull-off. (C) 2009 Elsevier Ltd. All rights reserved.

Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1 /| x | 2 . The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.

Compensation for compulsory acquisition of a licensed car parking space

The Acquisition of Land Act 1967 (Qld) (‘the Act’) deals with the acquisition of land by the State for public purposes and provides for compensation. The issue that arose for determination in Sorrento Medical Service Pty Ltd v Chief Executive, Dept of Main Roads [2007] QCA 73 was whether the appellant was entitled to claim compensation under the Act in respect of land resumed by the Main Roads Department over which the appellant had an exclusive contractual licence for car parking spaces for use in association with a medical centre leased by the appellant. At first instance, it was held by the Land Court that the appellant was not entitled to compensation for the resumption of the car parking spaces. The basis for this decision by the Land Court was that a right to compensation only exists where resumption has taken some proprietary interest of the claimant in the land. Following an appeal to the Land Appeal Court being dismissed, the appellant instituted the present appeal to the Queensland Court of Appeal (McMurdo P, Holmes JA and Chesterman J).

Place and Space: Community in the Internet Economy and What This Will Mean for Property

By 2020 Australia‟s National Digital Economy Strategy aims to increase household online participation and engage 12 per cent of all employees in teleworking arrangements. Achieving these goals is generally perceived as positive due to the reduced impact on the natural environment from less use of transport. However, this also will enable greater flexibility as to where people live and thus will impact upon the maintenance and formation of communities and on property use. This paper commences by clarifying what is Australia‟s internet economy before highlighting the impact of the internet on community formation and maintenance. The paper concludes by identifying what the achievement of these goals will mean for property use in the future.

“A problem of versions” : laying down the law in the school playground

Purpose This chapter investigates an episode where a supervising teacher on playground duty asks two boys to each give an account of their actions over an incident that had just occurred on some climbing equipment in the playground. Methodology This paper employs an ethnomethodological approach using conversation analysis. The data are taken from a corpus of video recorded interactions of children, aged 7-9 years, and the teacher, in school playgrounds during the lunch recess. Findings The findings show the ways that children work up accounts of their playground practices when asked by the teacher. The teacher initially provided interactional space for each child to give their version of the events. Ultimately, the teacher’s version of how to act in the playground became the sanctioned one. The children and the teacher formulated particular social orders of behavior in the playground through multi-modal devices, direct reported speech and scripts. Such public displays of talk work as socialization practices that frame teacher-sanctioned morally appropriate actions in the playground. Value of paper This chapter shows the pervasiveness of the teacher’s social order, as she presented an institutional social order of how to interact in the playground, showing clearly the disjunction of adult-child orders between the teacher and children.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Space, place and power : the spatial turn in literacy research

Place matters to literacy because the meanings of our language and actions are always materially and socially placed in the world (Scollon & Scollon, 2003). We cannot interpret signs, whether an icon, symbol, gesture, word, or action, without taking into account their associations with other meanings and objects in places. This chapter maps an emergent strand of literacy research that foregrounds place and space as constitutive, rather than a backdrop for the real action. Space and place are seen as relational and dynamic, not as fixed and unchanging. Space and place are socially produced, and hence, can be contested, re-imagined and re-made. In bringing space and place into the frame of literacy studies we see a subtle shift – a rebalancing of the semiotic with the materiality of lived, embodied, and situated experience. ...

Human rights, the law, cyber-security and democracy : after the European Convention

Many commentators have treated the internet as a site of democratic freedom and as a new kind of public sphere. While there are good reasons for optimism, like any social space digital space also has its dark side. Citizens and governments alike have expressed anxiety about cybercrime and cyber-security. In August 2011, the Australian government introduced legislation to give effect to Australia becoming a signatory to the European Convention on Cybercrime (2001). At the time of writing, that legislation is still before the Parliament. In this article, attention is given to how the legal and policy-making process enabling Australia to be compliant with the European Convention on Cybercrime came about. Among the motivations that informed both the development of the Convention in Europe and then the Australian exercise of legislating for compliance with it was a range of legitimate concerns about the impact that cybercrime can have on individuals and communities. This article makes the case that equal attention also needs to be given to ensuring that legislators and policy makers differentiate between legitimate security imperatives and any over-reach evident in the implementation of this legislation that affects rule of law principles, our capacity to engage in democratic practices, and our civic and human rights.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Panem et circenses : law, law and power in The Hunger Games

Like many cautionary tales, The Hunger Games takes as its major premise an observation about contemporary society, measuring its ballistic arc in order to present graphically its logical conclusions. The Hunger Games gazes back to the panem et circenses of Ancient Rome, staring equally cynically forward, following the trajectory of reality television to its unbearably barbaric end point – a sadistic voyeurism for an effete elite of consumers. At each end of the historical spectrum (and in the present), the prevailing social form is Arendt’s animal laborans. Consumer or consumed, Panem’s population is (with the exception of the inner circle) either deprived of the possibility of, or distracted from, political action. Within the confines of the Games themselves, Law is abandoned or de‐realised: Law – an elided Other in the pseudo‐Hobbesian nightmare that is the Arena. The Games are played out, as were gladiatorial combats and other diversions of the Roman Empire, against a background resonant of Juvenal’s concern for his contemporaries’ attachment to short term gratification at the expense the civic virtues of justice and caring which are (or would be) constitutive of a contemporary form of Arendt’s homo politicus. While the Games are, on their face, ‘reality’ they are (like the realities presented in contemporary reality television) a simulated reality, de‐realised in a Foucauldian set design constructed as a distraction for Capitol, and for the residents of the Districts, a constant reminder of their subservience to Capitol. Yet contemporary Western culture, for which manipulative reality TV is but a symptom of an underlying malaise, is inscribed at least as an incipient Panem, Its public/political space is diminished by the effective slavery of the poor, the pre‐occupation with and distractions of materiality and modern media, and the increasing concentration of power/wealth into a smaller proportion of the population.